Study of three quasi-two-body channels from $pi$$sup +$p interactions at 3.9 GeV/c

The $p{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ and $p{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ final states from ${\ensuremath{\pi}}^{+}p$ interactions at 3.9 GeV/c have been analyzed by the prism-plot technique and the following three quasi-two-body channels have been studied in detail: ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}p$, ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\Delta}}^{++}$, and ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\Delta}}^{++}$. Results are presented on cross sections, differential cross sections, and single and joint spin density matrix elements. These are compared with the Dar-Watts-Weisskopf absorption model and Reggeized pion-exchange model predictions. Relations among joint spin density matrix elements for ${\ensuremath{\rho}}^{0}{\ensuremath{\Delta}}^{++}$ are compared with quark-model predictions.